Lots of anger and excitement over this order. A lot of conservatives feel that they get unfairly censored or edited over social media and the White House has been publicly gathering evidence of double standards for the past couple years.
Recently Twitter "fact checked" a Trump tweet about mail in voting being an invitation for voter fraud. This is what prompted the executive order but it's been in the works for years.
The argument is simple: if a social media company (and this may apply to forums as well, most notably Reddit) chooses to "editorialize" people's content, then that makes them a "publisher" and not a "platform". In order to be a platform, they have to apply their rules in a neutral manner, not edit other's content and only remove content which is "flagrantly offensive" which presumably would not extend to things like debates over vote-by-mail elections.
The most obvious next move by social media companies is to expand the definition of what is considered flagrantly offensive but that might backfire in the long run since accusing people of anything you can censor might be defamation. For example then, if you can censor someone for saying that something is "racist" you might in theory also be sued for calling something racist.
Another response I've seen is "Trump is attacking Twitter's free speech" but this is also a losing argument because if Twitter's free speech is happening in the context of them editing other people's postings, that is basically an admission that they are editorializing.
FCC Chairman Ajit Pai, already hated for his stance on net neutrality, has received the executive order and presumably has some things that were mostly written last year ready to go.